Coupling of the Rice Convection Model
to global MHD codes
S. Sazykin, R. A. Wolf, F. R. Toffoletto, R. W. Spiro (Rice University)
D. L. De Zeeuw, G. Toth, T. Gombosi, A. Ridley (University of Michigan)
J. Lyon (Dartmouth College), M. Wiltberger (NCAR/HAO)
Why?
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GGCM=Geospace General Circulation Model, main eventual goal of
GEM)
Early idea within GEM was to use a modular approach, where different
regions with different physics processes are treated separately and then
they all are put together in some fashion
Later, global MHD codes were suggested as a “backbone” for a GGCM
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Global MHD are first-principles models that come closer to GGCM idea
Appear to simulate (imitate) some of the fundamental magnetospheric
physics phenomena
However, some important regions such as the ring current/inner
magnetosphere are not treated properly by global MHD due to breaking
approximations and numerical reasons.
Come up with a “coupled” model that it “almost” first-principles and
has an inner magnetosphere module that “corrects” ideal MHD
equations to account for gradient/curvature drift physics—the two
approaches can be complimentary.
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What is involved: Global Ideal MHD
• Modeling region extends from the upstream solar wind to ~200 RE
down the magnetotail. Region close to the Earth (R<2-3 RE) is usually
excluded for numerical reasons.
• Ideal MHD equations are integrated in time and space by different
numerical methods in different codes.
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Global Ideal MHD: Why do they need an inner
magnetosphere module?
• Global MHD codes don’t include gradient/curvature drift physics in
the ring current region. Single-fluid approximation is invalid.
• Inner magnetospheric pressure is too low (no ring current).
• Inner plasma sheet is too cold
• Region close to the Earth is difficult to model with adequate
resolution.
• Region-2 Birkeland currents, which
are generated at the inner edge of the
plasma sheet via pressure gradients.
Region-1 currents, which map out to
high-latitude plasma sheet boundary
and the magnetopause, are OK.
Iijima and Potemra, 1978
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Model of Inner Magnetosphere: RCM
• The RCM is limited to the slow-flow, quasi-static-equilibrium region
of the magnetosphere.
– Treats electrons and ions separately and splits the particle distribution into
dozens or hundreds of energy channels so that transport by
gradient/curvature drift can be included accurately.
– Often set out boundary at ~ 8-10 RE from Earth. The potential and plasma
distribution function needs to be specified on this boundary.
– Self-consistent within its regime, except that it doesn’t calculate B.
• 2-D model in terms of magnetic field-line integrated quantities:
– pressure is assumed isotropic along magnetic field lines-- V   ds/B
s  WsV 2 / 3 ;  s  nsV ; P  2 / 3V 2 / 3  s s
s
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RCM Equations
• Particle advection equations:


  B    (s / qs )V 2 / 3




 t
 s   L
2
B


• Ionospheric potential:
   ˆ     c   bˆ  V  P
• Model needs B-field everywhere and boundary conditions on the
E-field and particle fluxes as a function of time. These could be
taken from a global MHD code.
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How?
• The RCM is limited to the slow-flow, quasi-static-equilibrium region
of the magnetosphere lying on closed magnetic field lines.
– Pressure is constant along field lines.
– The potential and plasma distribution function needs to be specified on the
high-latitude boundary.
– Extensive field-line integration is required.
• MHD feeds the RCM information on
– Magnetic field in inner magnetosphere
– Boundary conditions
• RCM feeds back
– Inner-magnetospheric pressures (and eventually densities)
• The flow of information between the codes is complicated, because
they use very different formulations and very different grids.
• Either routine can compute Birkeland currents and potentials in RCM
region.
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History of “coupling” projects with RCM
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Mid-1990s: RCM coupled 2-way to the MRC global MHD code.
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Actual coupling was done (a module within MHD)
Code used MHD electric field in the RCM region
The largest difficulty was in the enormous amounts of time required to
trace magnetic field lines in the complicated 3-D grid of the MHD code.
Code ran, no science results
Mid-1990s: one-way LFM-RCM coupling
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Use LFM steady-state solution to drive the RCM
Trivial coupling (via writing/reading files).
Resulted in an M.S. thesis
Showed some of big difficulties lying ahead
A plan was suggested to for LFM to carry a second, B-field-aligned grid
for the RCM (never implemented).
Tests indicated that even cold plasma sheet in the LFM should generate
well-defined (but not realistic) region-2 currents.
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Example of an early 1-way LFM-RCM coupling
Birkeland currents into the ionosphere added for both hemispheres at t=0 (left) and
t=8 hrs (right), for the case of “cold” plasma in the RCM. Currents are in A/m2.
M. Hojo, Rice M.S. Thesis, 1997
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History of “coupling” projects with RCM
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2000 to present: RCM and J. Raeder’s MHD code
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1999 to present: coupling of RCM to BATSRUS
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Code coupling (RCM is part of MHD)
One-way: MHD drives the RCM.
Work in progress...
Code ran, no science results
Full two-way coupling as part of developing a “Sun-to-mud” first
principles computational model.
RCM was re-written for the project (including parallelization)
First publication was submitted Nov. 2003 to JGR (De Zeeuw et al).
Code is available for scientific investigations
2002 to present: coupling of RCM to LFM
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Part of CISM project, for which LFM is a “backbone”.
First results were obtained last Friday, but the code does not work yet.
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Adaptive Mesh Refinement
Coupling: Parallel Ray Tracing
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Conversion from MHD 3-D B, P, and  to 2-D RCM field-line integrated
quantities requires tracing (and integrating along) B lines on the RCM 2-D
ionospheric grid every coupling time step (1-10 min). Straightforward tracing
is not desirable because:
– Slow
– Technically difficult on a mesh with AMR.
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A novel technique (Toth-DeZeeuw) was invented to solve this problem
efficiently.
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Interpolated Tracing Algorithm
1. Trace lines inside blocks
starting from faces.
2. Interpolate and
communicate mapping.
3. Repeat 2. until the mapping
is obtained for all faces.
4. Trace lines inside blocks
starting from cell centers.
5. Interpolate mapping to
cell centers.
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… and this is where tracing is needed:
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Physics of coupled BATS-R-US—RCM model
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Two Way Coupling between BATS-R-US and RCM
The pressure that is fed back to the MHD code
by the RCM is used to drive the MHD pressure.
 Pressure is fed back on RCM grid
 Pressure is interpolated to the
MHD grid
 Comparison between MHD and
RCM pressures with the driver
computed as:
n 1
n
pMHD
 pMHD


t
p


RCM
n
 pMHD

 is usually on the order of 100t
so with each iteration there is a
≈1% change made in the MHD
pressure on closed field lines
within about 10 RE.
Run Description
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Steady solar wind conditions: IMF Bx=By=0, Bz=-5 nT.
At T=8 hours, Bz=-5 nT+5 nT suddenly at upstream boundary (Xgsm=32 RE).
Ionospheric conductances: P=4 S, H=0 in MHD and RCM. There is no auroral
zone enhancement to  (problem with grid overlap).
Full 2-way MHD-RCM coupling every 10 seconds.
854,016 computational cells are used in the MHD grid (smallest: 0.25 RE,
largest: 8 RE).
Inner boundary for MHD is at 2.5 RE (3.5 RE for mapping J||)
MHD (IONO) solves for the potential, RCM uses its own potential to move
particles but no direct feedback.
No dipole tilt.
Second run is same but without the RCM (pure MHD).
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Grid overlay
Plasma pressure build up during period of IMF Bz=-5 nT:
Equatorial plane view
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Grid overlay
Plasma pressure build up and magnetic field (white lines) stretching
during period of IMF Bz=-5 nT: Noon-midnight merid. plane view
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Plasma pressure symmetrizes after northward turning
After 8 hrs of strong driving,
pressure has a peak at ~4 Re
at midnight
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… and becomes much more
Following northward Bz
turning, pressure weakens on symmetric in MLT 2 hrs later.
the night side
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Plasma pressure and magnetic field (white lines) after northward turning:
Pressure symmetrizes, B-field dipolarizes
After 8 hrs of strong driving,
magnetic field lines on the
night side are highly
stretched.
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Following northward Bz
turning, magnetic field
becomes “less stretched”…
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… and becomes much more
dipolar-like after 2 hrs,
consistent with magnetic field
and plasma being in
approximate force-balance.
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Plasma sheet temperature (whole run): Equatorial plane view
Before coupling is
established, plasma sheet is
unrealistically cold (typical
of MHD only)
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After 8 hrs of Bz<0 driving,
plasma sheet within 10 RE is
much warmer (more
realistic)
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After northward turning, tail
B-field dipolarizes, further
increasing plasma
temperature in the ring
current.
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M-I coupling electrodynamics during Bz<0 period:
Formation of realistic region-2 Birkeand currents
Without RCM, MHD has negligible
region-2 field-aligned currents, and
convection electric field is not shielded
from low latitudes (equipotentials
“leak” to lower lats.
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In a steady-state with RCM coupling,
region-2 currents are of magnitudes
similar to region-1, and there is
noticeable shielding (convection
pattern is more confined to auroral
zone).
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M-I coupling electrodynamics after Bz>0 turning:
Overshielding by region-2 currents
At the time of northward
turning, strong convection,
well-developed region-2
currents, strong shielding.
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After northward turning,
overshielding pattern
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…that eventually settles
down to a weaker convection
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Is P really constant along B-field lines?
Outside 3.5 RE, projected B-field lines tend to be parallel to contours of
constant pressure. Closer to Earth, deviations do not have much effect:
B-field
vectors are
of same
length!
J||~grad(V), and V is contained near the equatorial plane. For a dipole
field, 75% of V comes from between 0.84R0 and R0.
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Role of R-2 FAC in determining PCP drop
Hill et al. [1976], and Siscoe et al. [2002]: PCP drop
is limited by region-1 FAC:
Siscoe et al. [2002] also predicted that having region-2 FAC
in MHD models would reduce PCP due to increased effective
conductance.
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Region-2 currents due to RCM coupling provide an additional
closure path for region-1 currents, thus modifying PCP drop.
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Time History of PCP drop with and without RCM coupling
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• CISM Project
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LFM-RCM: Initial 2-way coupling
• First 2-way coupling has been done. The two codes are run
independently and exchange information via writing/reading files.
• The ultimate goal is to use the InterComm library (software package)
that allows different codes to exchange information. This does not
require re-writing existing large computer codes. The current scheme
of coupling via files was designed to mimic InterComm-style
information exchange before InterComm became available.
• Magnetic field-line tracing is done by re-interpolating MHD and RCM
data structures on an intermediate 3-D rectangular grid. Since the
version of the LFM used is an OpenMP code, this works well, but it is
not clear if this is suitable in the future.
• LFM supplies to the RCM 1-minute average physical quantities, and
the RCM overwrites P and .
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LFM-RCM: Initial Trial Run
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Steady-state conditions.
IMF Bz=-5 nT
LFM inner boundary at 2.5 RE.
Ionospheric conductances are
supplied by LFM.
• Coupling time is 1 min.
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LFM-RCM
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During 1 hour of coupled simulation, a partial ring current begins to form and the
corresponding inflation in the magnetic field can be seen.
Pressure increase at ~8 RE is up to 4 nPa.
However, there are instabilities problems arising in the LFM, the nature of then is not clear yet.
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LFM-RCM 2-way coupling:
In this short run, region-2 currents begin to form in the RCM after ~1 hr.
Work is in progress...
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Summary
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Technically challenging problem. Not clear if it can be done at all.
Work on BATSRUS-RCM started ~5 years ago, and very good progress has
been made (there is a working code available for science investigations).
Work on LFM-RCM started <2 years ago (CISM), and initial results are just
now being obtained.
The process can be broken down into 3 levels:
– Level 0: achieve increase in P, formation of a partial ring current, and inflation of B
in global MHD codes, also formation of region-2 currents (most difficult). Done
with BATSRUS, in progress with LFM.
– Level 1: design a self-consistent way to handle ionospheric electric field and
conductances in both codes (we know how to do it, about to be done with
BATSRUS. Work under way with LFM, but it goes beyond the RCM).
– Level 2: further additions to codes, such as diffuse auroral precipitation, fieldaligned potential drops, anisotropic pressure in the RCM. Not clear how to do,
mostly have not thought about it.
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Instabilities possibly related to coupling are not understood well, although they
seem to be common to more than one coupled code and may be a physical
property of the magnetospheric system.
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Science Applications
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We are applying BATSRUS-RCM to the problem of time-dependence of
prompt-penetration ionospheric electric fields. It can only be done with a
coupled code.
We are estimating the induction electric fields in the RCM within the coupled
BATSRUS-RCM code in view of their possible role on plasmaspheric
structuring observed by IMAGE EUV.
Aside from some missing pieces, we now have computational capability to
solve a complete and reasonably defensible set of equations for the inner
magnetosphere. MHD codes model the coupling between the magnetosphere
and solar wind, which eliminates the need for a lot of boundary conditions in
the RCM, which are not available directly from observations.
It may be time to start attacking the problem of magnetic storms, substorms,
and related phenomena (sawtooth events, etc) with these coupled codes,
assuming that MHD codes model non-adiabatic processes in a way the Nature
does. Possibly will need some sort of data assimilation.
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Some Specific Science Questions
• Some sample scientific questions:
– What are the essential non-adiabatic processes that occur in the middle
plasma sheet at substorm onset? We can’t treat the kinetic processes in
detail in these large-scale codes, but if we can parameterize their effects
and achieve agreement with observations, that will place very strong
constraints on the microphysical processes.
– What causes auroral breakup, westward traveling surge? Do these follow
automatically from appropriate non-adiabatic reduction of PV5/3, given an
appropriate algorithm for estimating field-aligned potential drops?
– Same for the dispersion signatures observed in particles at
geosynchronous orbit in a substorm.
– What is the role of the magnetospheric interchange instability in
producing the observed features of substorms and storms, particularly as
reflected in auroral emission patterns?
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